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SUMMARY:David Hansen (Max Planck Institute for Mathematics)
DTSTART:20211014T160000Z
DTEND:20211014T172000Z
DTSTAMP:20260423T052755Z
UID:RAMpAGe/53
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/RAMpAGe/53/"
 >Bun_G minicourse:  The Kottwitz conjecture</a>\nby David Hansen (Max Plan
 ck Institute for Mathematics) as part of Recent Advances in Modern p-Adic 
 Geometry (RAMpAGe)\n\n\nAbstract\nThis talk is the fourth part of a six-pa
 rt series "$\\mathrm{Bun}_G$\, Shtukas\, and the Local Langlands Program"\
 , held Tuesdays and Thursdays between 5 and 21 October\, 2021.\n\nRecordin
 gs and slides will appear here:  https://sites.google.com/view/rampagesemi
 nar/home\n\nSeries abstract:  The recent manuscript of Fargues-Scholze aim
 s to "geometrize" the Langlands program for a p-adic group $G$\, by relati
 ng the players in that story to the stack $\\mathrm{Bun}_G$.  Following a 
 strategy of V. Lafforgue\, the main result of [FS] is the construction of 
 an L-parameter attached to a smooth irreducible representation of $G$.\n\n
 The goal of this series is to review the main ideas of this work\, and to 
 discuss two related results:  progress on the Kottwitz conjecture for loca
 l shtuka spaces by Hansen-Kaletha-Weinstein\,  and the construction of eig
 ensheaves on $\\mathrm{Bun}_G$ when $G=\\mathrm{GL}_n$ by Anschütz-le Bra
 s. \n\nTalk abstract: In this lecture\, we will give a detailed sketch of 
 the proof of the main theorem of [HKW]\, building on the material in the f
 irst three lectures.  The idea that the Kottwitz conjecture should follow 
 from some form of the Lefschetz trace formula goes back to Harris in the '
 90s. We will try to emphasize the new ingredients which allow us to implem
 ent this idea in full generality.\n
LOCATION:https://researchseminars.org/talk/RAMpAGe/53/
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